Answer:
The measure of angle LJC is [tex]m\angle LJC=43\°[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of arc LC
we know that
[tex]arc\ LC+arc\ JC=180\°[/tex] ----> because the diameter divide the circle into two equal parts
substitute the given values
[tex]arc\ LC+94\°=180\°[/tex]
[tex]arc\ LC=180\°-94\°=86\°[/tex]
step 2
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m\angle LJC=\frac{1}{2}[arc\ LC][/tex]
substitute
[tex]m\angle LJC=\frac{1}{2}[86\°]=43\°[/tex]
